{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vertical takeoff and landing aircraft\n",
    "\n",
    "This notebook demonstrates the use of the python-control package for analysis and design of a controller for a vectored thrust aircraft model that is used as a running example through the text *Feedback Systems* by Astrom and Murray. This example makes use of MATLAB compatible commands. \n",
    "\n",
    "Additional information on this system is available at\n",
    "\n",
    "http://www.cds.caltech.edu/~murray/wiki/index.php/Python-control/Example:_Vertical_takeoff_and_landing_aircraft"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## System Description\n",
    "This example uses a simplified model for a (planar) vertical takeoff and landing aircraft (PVTOL), as shown below:\n",
    "\n",
    "![PVTOL diagram](https://murray.cds.caltech.edu/images/murray.cds/7/7d/Pvtol-diagram.png)\n",
    "\n",
    "![PVTOL dynamics](https://murray.cds.caltech.edu/images/murray.cds/b/b7/Pvtol-dynamics.png)\n",
    "\n",
    "The position and orientation of the center of mass of the aircraft is denoted by $(x,y,\\theta)$,  $m$ is the mass of the vehicle, $J$ the moment of inertia, $g$ the gravitational constant and $c$ the damping coefficient. The forces generated by the main downward thruster and the maneuvering thrusters are modeled as a pair of forces $F_1$ and $F_2$ acting at a distance $r$ below the aircraft (determined by the geometry of the thrusters).\n",
    "\n",
    "Letting $z=(x,y,\\theta, \\dot x, \\dot y, \\dot\\theta$), the equations can be written in state space form as:\n",
    "$$\n",
    "\\frac{dz}{dt} = \\begin{bmatrix}\n",
    "                       z_4 \\\\\n",
    "                       z_5 \\\\\n",
    "                       z_6 \\\\\n",
    "                       -\\frac{c}{m} z_4 \\\\\n",
    "                       -g- \\frac{c}{m} z_5 \\\\\n",
    "                       0\n",
    "                  \\end{bmatrix}\n",
    "                  +\n",
    "                  \\begin{bmatrix}\n",
    "                       0 \\\\\n",
    "                       0 \\\\\n",
    "                       0 \\\\\n",
    "                       \\frac{1}{m} \\cos \\theta F_1 + \\frac{1}{m} \\sin \\theta F_2 \\\\\n",
    "                       \\frac{1}{m} \\sin \\theta F_1 + \\frac{1}{m} \\cos \\theta F_2 \\\\\n",
    "                       \\frac{r}{J} F_1\n",
    "                  \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "## LQR state feedback controller\n",
    "This section demonstrates the design of an LQR state feedback controller for the vectored thrust aircraft example. This example is pulled from Chapter 6 (Linear Systems, Example 6.4) and Chapter 7 (State Feedback, Example 7.9) of [Astrom and Murray](https://fbsbook.org). The python code listed here are contained the the file pvtol-lqr.py.\n",
    "\n",
    "To execute this example, we first import the libraries for SciPy, MATLAB plotting and the python-control package:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *             # Grab all of the NumPy functions\n",
    "from matplotlib.pyplot import * # Grab MATLAB plotting functions\n",
    "from control.matlab import *    # MATLAB-like functions\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters for the system are given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 4                         # mass of aircraft\n",
    "J = 0.0475                    # inertia around pitch axis\n",
    "r = 0.25                      # distance to center of force\n",
    "g = 9.8                       # gravitational constant\n",
    "c = 0.05                      # damping factor (estimated)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choosing equilibrium inputs to be $u_e = (0, mg)$, the dynamics of the system $\\frac{dz}{dt}$, and their linearization $A$ about equilibrium point $z_e = (0, 0, 0, 0, 0, 0)$ are given by\n",
    "$$\n",
    "\\frac{dz}{dt} = \\begin{bmatrix}\n",
    "                       z_4 \\\\\n",
    "                       z_5 \\\\\n",
    "                       z_6 \\\\\n",
    "                       -g \\sin z_3 -\\frac{c}{m} z_4 \\\\\n",
    "                       g(\\cos z_3 - 1)- \\frac{c}{m} z_5 \\\\\n",
    "                       0\n",
    "                  \\end{bmatrix}\n",
    "\\qquad\n",
    "A = \\begin{bmatrix}\n",
    "       0 & 0 & 0 &1&0&0\\\\\n",
    "       0&0&0&0&1&0 \\\\\n",
    "       0&0&0&0&0&1 \\\\\n",
    "       0&0&-g&-c/m&0&0 \\\\\n",
    "       0&0&0&0&-c/m&0 \\\\\n",
    "       0&0&0&0&0&0\n",
    "    \\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# State space dynamics\n",
    "xe = [0, 0, 0, 0, 0, 0]         # equilibrium point of interest\n",
    "ue = [0, m*g]                   # (note these are lists, not matrices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dynamics matrix (use matrix type so that * works for multiplication)\n",
    "# Note that we write A and B here in full generality in case we want\n",
    "# to test different xe and ue.\n",
    "A = matrix(\n",
    "   [[ 0,    0,    0,    1,    0,    0],\n",
    "    [ 0,    0,    0,    0,    1,    0],\n",
    "    [ 0,    0,    0,    0,    0,    1],\n",
    "    [ 0, 0, (-ue[0]*sin(xe[2]) - ue[1]*cos(xe[2]))/m, -c/m, 0, 0],\n",
    "    [ 0, 0, (ue[0]*cos(xe[2]) - ue[1]*sin(xe[2]))/m, 0, -c/m, 0],\n",
    "    [ 0,    0,    0,    0,    0,    0 ]])\n",
    "\n",
    "# Input matrix\n",
    "B = matrix(\n",
    "   [[0, 0], [0, 0], [0, 0],\n",
    "    [cos(xe[2])/m, -sin(xe[2])/m],\n",
    "    [sin(xe[2])/m,  cos(xe[2])/m],\n",
    "    [r/J, 0]])\n",
    "\n",
    "# Output matrix \n",
    "C = matrix([[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]])\n",
    "D = matrix([[0, 0], [0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute a linear quadratic regulator for the system, we write the cost function as\n",
    "$$ J = \\int_0^\\infty (\\xi^T Q_\\xi \\xi + v^T Q_v v) dt,$$\n",
    "\n",
    "where $\\xi = z - z_e$ and $v = u - u_e$ represent the local coordinates around the desired equilibrium point $(z_e, u_e)$. We begin with diagonal matrices for the state and input costs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Qx1 = diag([1, 1, 1, 1, 1, 1])\n",
    "Qu1a = diag([1, 1])\n",
    "(K, X, E) = lqr(A, B, Qx1, Qu1a); K1a = matrix(K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a control law of the form $v = -K \\xi$, which can then be used to derive the control law in terms of the original variables:\n",
    "\n",
    "\n",
    "  $$u = v + u_e = - K(z - z_d) + u_d.$$\n",
    "where $u_e = (0, mg)$ and $z_d = (x_d, y_d, 0, 0, 0, 0)$\n",
    "\n",
    "The way we setup the dynamics above, $A$ is already hardcoding $u_d$, so we don't need to include it as an external input. So we just need to cascade the $-K(z-z_d)$ controller with the PVTOL aircraft's dynamics to control it. For didactic purposes, we will cheat in two small ways:\n",
    "\n",
    "- First, we will only interface our controller with the linearized dynamics. Using the nonlinear dynamics would require the `NonlinearIOSystem` functionalities, which we leave to another notebook to introduce.\n",
    "2. Second, as written, our controller requires full state feedback ($K$ multiplies full state vectors $z$), which we do not have access to because our system, as written above, only returns $x$ and $y$ (because of $C$ matrix). Hence, we would need a state observer, such as a Kalman Filter, to track the state variables. Instead, we assume that we have access to the full state.\n",
    "\n",
    "The following code implements the closed loop system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Our input to the system will only be (x_d, y_d), so we need to\n",
    "# multiply it by this matrix to turn it into z_d.\n",
    "Xd = matrix([[1,0,0,0,0,0],\n",
    "             [0,1,0,0,0,0]]).T\n",
    "\n",
    "# Closed loop dynamics\n",
    "H = ss(A-B*K,B*K*Xd,C,D)\n",
    "\n",
    "# Step response for the first input\n",
    "x,t = step(H,input=0,output=0,T=linspace(0,10,100))\n",
    "# Step response for the second input\n",
    "y,t = step(H,input=1,output=1,T=linspace(0,10,100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(t,x,'-',t,y,'--')\n",
    "plot([0, 10], [1, 1], 'k-')\n",
    "ylabel('Position')\n",
    "xlabel('Time (s)')\n",
    "title('Step Response for Inputs')\n",
    "legend(('Yx', 'Yy'), loc='lower right')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above shows the $x$ and $y$ positions of the aircraft when it is commanded to move 1 m in each direction. The following shows the $x$ motion for control weights $\\rho = 1, 10^2, 10^4$. A higher weight of the input term in the cost function causes a more sluggish response. It is created using the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Look at different input weightings\n",
    "Qu1a = diag([1, 1])\n",
    "K1a, X, E = lqr(A, B, Qx1, Qu1a)\n",
    "H1ax = H = ss(A-B*K1a,B*K1a*Xd,C,D)\n",
    "\n",
    "Qu1b = (40**2)*diag([1, 1])\n",
    "K1b, X, E = lqr(A, B, Qx1, Qu1b)\n",
    "H1bx = H = ss(A-B*K1b,B*K1b*Xd,C,D)\n",
    "\n",
    "Qu1c = (200**2)*diag([1, 1])\n",
    "K1c, X, E = lqr(A, B, Qx1, Qu1c)\n",
    "H1cx = ss(A-B*K1c,B*K1c*Xd,C,D)\n",
    "\n",
    "[Y1, T1] = step(H1ax, T=linspace(0,10,100), input=0,output=0)\n",
    "[Y2, T2] = step(H1bx, T=linspace(0,10,100), input=0,output=0)\n",
    "[Y3, T3] = step(H1cx, T=linspace(0,10,100), input=0,output=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(T1, Y1.T, 'b-', T2, Y2.T, 'r-', T3, Y3.T, 'g-')\n",
    "plot([0 ,10], [1, 1], 'k-')\n",
    "title('Step Response for Inputs')\n",
    "ylabel('Position')\n",
    "xlabel('Time (s)')\n",
    "legend(('Y1','Y2','Y3'),loc='lower right')\n",
    "axis([0, 10, -0.1, 1.4])\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lateral control using inner/outer loop design\n",
    "This section demonstrates the design of loop shaping controller for the vectored thrust aircraft example. This example is pulled from Chapter 11 (Frequency Domain Design) of [Astrom and Murray](https://fbsbook.org). \n",
    "\n",
    "To design a controller for the lateral dynamics of the vectored thrust aircraft, we make use of a \"inner/outer\" loop design methodology. We begin by representing the dynamics using the block diagram\n",
    "\n",
    "<img src=https://murray.cds.caltech.edu/images/murray.cds/3/3f/Pvtol-lateraltf.png>\n",
    "\n",
    "The controller is constructed by splitting the process dynamics and controller into two components: an inner loop consisting of the roll dynamics $P_i$ and control $C_i$ and an outer loop consisting of the lateral position dynamics $P_o$ and controller $C_o$.\n",
    "<img src=https://murray.cds.caltech.edu/images/murray.cds/f/f1/Pvtol-nested-1.png>\n",
    "The closed inner loop dynamics $H_i$ control the roll angle of the aircraft using the vectored thrust while the outer loop controller $C_o$ commands the roll angle to regulate the lateral position.\n",
    "\n",
    "The following code imports the libraries that are required and defines the dynamics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import * # Grab MATLAB plotting functions\n",
    "from control.matlab import *    # MATLAB-like functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# System parameters\n",
    "m = 4                         # mass of aircraft\n",
    "J = 0.0475                    # inertia around pitch axis\n",
    "r = 0.25                      # distance to center of force\n",
    "g = 9.8                       # gravitational constant\n",
    "c = 0.05                      # damping factor (estimated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transfer functions for dynamics\n",
    "Pi = tf([r], [J, 0, 0])       # inner loop (roll)\n",
    "Po = tf([1], [m, c, 0])       # outer loop (position)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the inner loop, use a lead compensator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 200\n",
    "a = 2\n",
    "b = 50\n",
    "Ci = k*tf([1, a], [1, b])     # lead compensator\n",
    "Li = Pi*Ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The closed loop dynamics of the inner loop, $H_i$, are given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "Hi = parallel(feedback(Ci, Pi), -m*g*feedback(Ci*Pi, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we design the lateral compensator using another lead compenstor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now design the lateral control system\n",
    "a = 0.02\n",
    "b = 5\n",
    "K = 2\n",
    "Co = -K*tf([1, 0.3], [1, 10])         # another lead compensator\n",
    "Lo = -m*g*Po*Co"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance of the system can be characterized using the sensitivity function and the complementary sensitivity function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = Co*Hi*Po\n",
    "S = feedback(1, L)\n",
    "T = feedback(L, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, y = step(T, T=linspace(0,10,100))\n",
    "plot(y, t)\n",
    "title(\"Step Response\")\n",
    "grid()\n",
    "xlabel(\"time (s)\")\n",
    "ylabel(\"y(t)\")\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frequency response and Nyquist plot for the loop transfer function are computed using the commands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bode(L)\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nyquist(L, (0.0001, 1000))\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gangof4(Hi*Po, Co)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
